Radial velocity observations of the 2015 Mar 20 eclipse - A benchmark Rossiter-McLaughlin curve with zero free parameters

On March 20, 2015, we obtained 159 spectra of the Sun as a star with the solar telescope and the FTS at the Institut f\"ur Astrophysik G\"ottingen, 76 spectra were taken during partial solar eclipse. We obtained RVs using $I_2$ as wavelength reference and determined the RM curve with a peak-to-peak amplitude of almost 1.4 km s$^{-1}$ at typical RV precision better than 1 m s$^{-1}$. We modeled disk-integrated solar RVs using surface velocities, limb darkening, and information about convective blueshift from 3D magneto-hydrodynamic simulations. We confirm that convective blueshift is crucial to understand solar RVs during eclipse. Our best model reproduced the observations to within a relative precision of 10% with residuals less than 30 m s$^{-1}$. We cross-checked parameterizations of velocity fields using a Dopplergram from the Solar Dynamics Observatory and conclude that disk-integration of the Dopplergram does not provide correct information about convective blueshift necessary for m s$^{-1}$ RV work. As main limitation for modeling RVs during eclipses, we identified limited knowledge about convective blueshift and line shape as functions of solar limb angle. We suspect that our model line profiles are too shallow at limb angles larger than $\mu = 0.6$ resulting in incorrect weighting of the velocities across the solar disk. Alternative explanations cannot be excluded like suppression of convection in magnetic areas and undiscovered systematics during eclipse observations. Accurate observations of solar line profiles across the solar disk are suggested. We publish our RVs taken during solar eclipse as a benchmark curve for codes calculating the RM effect and for models of solar surface velocities and line profiles.